Welcome to TSAOpy’s site

Time Series by Anharmonic Oscillators is a Python library developed to fit user defined differential equations (with the form of anharmonic oscillators) to time series data.

What it does

Suppose we have sets of points making up time series such as

This library will allow us to propose a differential equation for the $x(t)$ function, and fit the free parameters to find a good differential equation that models the dynamics of the system.

Why doing this?

Running this analysis allows one to find a differential equation (DE) that a (or a set of) time series roughly obeys. Some interesting things that can be done with the DE are

1. Modelling of damping forces or potentials. One may associate each term of the DE with a certain term of the polynomial expansion of a potential or damping force, and thus getting approximations of the behaviour of your system’s potential or drag effects.
2. Non linear dynamics analysis. Finding the DE that the system obeys allows using some theoretical tools such as plotting phase portraits and phase space trajectories, finding limit cycles, analyzing stability, energy conservation, etc.

Set Up

• In order to make tsaopy work one should first be using a Linux PC, specifically it’s being developed and tested on Ubuntu 20+ systems. Windows won’t work, and we haven’t tried it on macOS.

• Necessary Python dependencies are numpy, and another package I developed (largely to serve as a base for tsaopy) which is quickemcee, which also depends on scipy, matplotlib, emcee, and corner.

• tsaopy uses a Fortran submodule in its backend. In order to compile it, it’s necessary that there’s a Fortran compiler, such as gfortran, installed and properly pathed. If there isn’t, then sudo apt-get install gfortran should do it.

• With this, it’s possible to install tsaopy using pip install tsaopy.

At this point tsaopy should be installed.

Note: some users may run into trouble if path variables for certain numpy submodules are not properly set up. However, it should work out of the box if you install everything in a new conda enviroment, and all the dependencies including Python itself are up to date.

If you have any problems during installation please make an issue in the Github repo with all the information you can gather.

Test installation

After running pip install tsaopy try opening a Python console and run import tsaopy. It may take a few seconds (the backend submodules are compiled the first time you import tsaopy). Should any errors arise, please report the issue.

If you can import tsaopy succesfully try running the basic test script. Go to the project’s repository test folder and either

• Download ‘basictest.py’ and run it from the Linux terminal with python basictest.py, or
• Copy the contents of the file and run them on a Python console.

If everything is working properly something like this should be displayed

Referencing TSAOpy

We have a Zenodo DOI set up for the repository for the time being

And this is my personal ORCID

The following Bibtex citation is recommended

@software{tsaopy,
  author       = {Scozziero, Sofía Anna},
  title        = {The TSAOpy library},
  month        = may,
  year         = 2022,
  publisher    = {Zenodo},
  doi          = {10.5281/zenodo.6569848},
  url          = {https://tsaopy.github.io/}
}

There will probably be an article or something of the sorts in the near future.